Atmospheric and topographic
correction of multitemporal Landsat TM imagery
Zhang Yugui The Research Institute of Forest
resource Information Chinese Academy of Forestry
Abstract The paper briefly introduced a developing
system for comprehensive correction satellite imagery. Standarized
reflectance images were produced by atmospheric correction, topographic
correction, sensor calibration etc. The atmospheric parameters parameters
were interpolated by using local meteorological records. The path radiance
derived from visual range is adjusted with dark pixels in the image data.
A digital topographic model was used both to correct for the
georadiometric effects and to monitor the optical thickness. The
normalized reflectance image were enhanced with linear or non-linear
transformation. A set of multitemporal subscenes of four dates in
Trolleba, Sweden were used as examples to illustrate the good
correspondence of correction results in quite different atmospheric
conditions.
Introduction The main factors that seriously
affect the radiometric quality of digital satellite data are atmospheric
attenuation and topographic distortion, in addition to sensor variation.
All these factors are related to and restrictive with each other.
Therefore, a correction algorithm that considers only a single digital
topographic model. The paper described a developing correction system
which made comprehensive correction of Landsat TM and other satellite
data, including sensor calibration, path radiance evaluation, the
calculation of attenuation coefficients of atmosphere, the variations of
direct solar illumination and diffuse illumination caused by topography,
as well as minor modifications of the components of optical thickness due
to calculate the needed atmospheric parameters by using metrological
records, and presented result ofthe calculation after these parameters
were input to the radiative transfer model of Turner.
The
multitemporal TM images used in this study consist of 4 subscenes of 400 X
400 pixels of the same Trollebo scene, located in south-central part of
sweden. The elevation of the area is from 164 to 285 meters ASL. Clear
water bodies are scattered over the whole area. The trollebo area contains
mainly forest lands with a small portion of agricultural fields. The four
dates constitute the whole growing season of forest vegetation , Pine,
spruce , birch and broadleaves make up the major forest type categories.
Table 1 listed the data of the 4 dates.
Table 1. Parameters for trollebo subscence. The scene
center coordinates, sun elevation azimuth and view angles are in
decimal degrees.
Scene |
Over pass time |
scene center coordinates |
sun azim |
sun elev |
view angle |
Sun-earth dist. (au) |
1 |
194/20:2 1984.4.27 09 35 39 |
(57.317,14.756) |
133.42 |
39.17 |
2.058 |
0.9932 |
2 |
194/20:2 1984.5.13 09 36 12 |
(57.819,14.718) |
131.47 |
43.47 |
2.733 |
0.9794 |
3 |
193/20 : 1984.7.09 09 27 05 |
(57.317,15.713) |
123.88 |
44.98 |
1.324 |
0.9670 |
4 |
193/20:2 1984.9.0209 39 38 |
(57.317,14.493) |
136.92 |
33.66 |
2.987 |
0.9827 | The correction
proceduresConceptually, the reflectance images can be obtained
through three sequential linear transformations.
- A Transformation From Digital Numbers (DN) To observed Spectral
Radiance Values (Lobs)
This is accomplished by using published
radiance calibration constants (Barker 1987), which is usually termed
absolute calibration. Spectral radiance and irradiance were used in the
study instead of in-band units throughout the computation procedures to
facilitate comparison between sensor (Price 1987).
The
Lobs can be obtained by
Lobs =
DN* (Lmax - Lmin) / 255
+Lmin ----------------(1)
Lmax -
Lmin are constants representing the radiance at DN= 0 and
DN=255, respectively. These constants may vary with date, ground
receiving and processing station. Before this tranformation, a relative
compensation calobration between etectors were performed for most
scenes.
- A Transformation From Radiance Lobs to Spectral
Reflectance R
It is complicated and critical. The assumption of a
Lambertian scattering behaviour for most targets would simplify the view
angle effect as only differential atmospheric effect. Therefore, the
correction of main interest is atmospheric and topographic corrections,
illumination and view angle corrections, in addition to sensor
calibration. The radiance observed by a sensor in a given band can be
expressed as
Lobs = 1 / p
(Eo cosi Exp(-t/cosqo) +gEd)R Exp(-t/cosqv ) +Lp ------(2)
or in a
simplified form
Lobs = 1/ p
R Eg Tv +Lp
and the transformed reflectance R for a
target can be expressed as
R= p
(Lobs- Lp ) / Eg Tv) ..............(3)
The meanings of various factors are defined as follows:
Lobs = radiance observed at the sensor
(mWcm-2 Sr-1)
1 / p = The bidirectional reflectance distribution
function (BRDF) for a Lambertian surface
Eo= solar irradiance at
the top of the atmosphere (m Wcm-2),
Eo was calibrated
with published solar exoatmospheric spectral irradiances in TM bands
Eo was calibrated with published solar exoatmospheric spectral
irradiances in TM bands
i= solar incidence angle with respect to
surface normal
t= atmospheric extinction coefficient (optical
thickness)
qo, qv = solar zenith angle and observation
zenith angle
g = a geometric factor taking into account of the
part of sky radiance not contributing in the illumination of inclined
terrain , g= 0.5+0.5coss, s=terrain slope angle
Ed =
diffuse sky irradiance on a horizontal surface (m Wcm-2) Ed
is modified by atmosphere and topography.
Eg= (Eo
cosi Tq+g Ed) = global irradiance on the
surface (m Wcm-2)
Tq =
exp(-t/cosqo) = atmospheric downward
transmittance
Tv = Exp (-t/ cosqv) = atmospheric up eard transmittance
Lp = path radiance from multiple scattering (m Wcm-2
sr-1 )
This reflectance tranformation involves the
approximation of some varibles by using different methods according to
parameters available . Combining equation (1) and (3) we obtain
R= p / (Eg Tv) *(DN(Lmax -
Lmin) / 255 +Lmin -Lp) -----(3a)
- A Transformation of R to an Eight-bit Digital Number
(DN')
It may be a linear or non-linear transformation,
incorporating appropriate contrast stretch between predefined minimum
and maximum reflectance limits Rmax - and Rmin
DN' = 255 F[(R-Rmin) / (Rmax -
Rmin)] ................(4)
The linear
transformation is convenient if the enhanced reflectance images are to
undergo further processing, but for the hard copy products, a non-linear
transformation can be applied to TM bands. The square root function
increases the contrast of low reflectance portion, and compress the
contrast of high reflectance portion (Ahern 1989).
Although each
step involves much consideration and techniques, the second step
requires more investigation and exploration. The actual scattering
properties of natural surfaces differ from the Lambertian assumption to
varying extent (Teillet et al. 1982) The diffuse approximation is more
likely to be valid for terrain slopes of less than 25 degrees and
effective illumination angles of less than 45 degrees (Smith et al.
1980) or further less (Cavayas 1987). In our study, the solar zenith
angle exceeded these limits, which may cause a system error of the
reflectance values. Since we have no sufficient knowledge about the BRDF
for natural targets, such assumption is the only convenient solution at
present, espescially for forest canopy complexities which are considered
to be Lambertian surface in small solar zenith angle.
Evaluation and computation of atmospheric parameters
The global irradiance E g, diffuse irradiance
E d and path radiance L p for the center wavelength of
TM bands were calculated with the Turner and Spencer (1972) reductive
transfer model, and with Forster's modification (1984) for the computation
of the single scattering phase function, after appropriate TM band
adjustment. This requires estimated or calculated optical thickness
t,solar zenith qo solar azimuth, nadir
view angle qv , view azimuth as input.
The scene center coordinates and scene center overpass time were used to
derive the components of optical thickness t. The radiative transfer model
provided convenience for establishing relationship between atmospheric
parameters. In the process of computing the parameters, the scale heights
for E d, E g and L p were determined, which
facilitate the computation procedures of corresponding values for each
pixel.
- The Estimation of Path Radiance
Lp
Lp is an important factor. In our study,
it was derived from radiative transfer model after computation of the
input meteorological data. However, several approaches can be applied to
evaluate Lp for the purpose of reference. Since clear water
bodies exist in the studied area, the dark pixel method (Ahern 1977) was
used due to its simplicity . The relative scattering function method
(chavez 1987 , 1988) is also convenient . The covariance matrix method
(Switzer 1981) and RIM ( Crippen 1987) require that spectrally
homogeneous targets being distributed over slopes of various aspects. In
this study, the Lp values were used to compare with those calculated by
using meteorological data, and to monitor and adjust the latter if they
were unreliable.
- Use of Local metrological records to Estimate optical
Thickness
The optical thickness t in equation (1) is a critical
coefficient and is affected by many factors. since the measurement of at
overpass time is seldom done, it is usually estimate some atmospheric
various methods meteorological records could be utilized to estimate
some atmospheric parameters. The daily records at 1,7,13 and 19 hours
include temperature, air pressures, water vapour pressure, relative
humidity, visibility, wind speed etc. The overpass time data were
derived from the interpolated data. The physical atmospheric thickness
was accounted for as function of topographic elevation. There fore the
station elevation ASL (above sea level) and the parameter values at the
station elevation were used to derive the scale heights of parameters,
which were applied to each pixel of the image when a topographic model
was available. The normal optical thickness t equals the sum of the
attenading coefficients, and they are independent. Therefore t is made
up of Rayleigh component tr due to molecular scattering, aerosol
component tp due to particle scattering, and components due to selective
absortption of gases, such as water wapour component tw,
ozone component toz, and carbon dioxide component tco2. All
these are wavelength dependent.
t = tr +
tp + tw + toz + tco2
+.......(5)
we deal with the t components separately. The Rayeigh
molecular scattering is regarded as of dry air, and the water absorption
as of partial pressure of water vapour, and the aersol scattering as of
suspending particles.
The visibility may be a measure of tp for
a particular vertical distribution . Turner (1972) graphed tp as a
function of visibility for continental atmosphere. We have interpolated
and extrapolated the graphs for TM bands with the central wavelength as
reference, and then an adjustment or alignment can be applied to the
interpolated tp values with shaded clear water pixel values
in TM band 4 as reference in the process of calculation. The
double usage of topographic modelThe inclusion of even a rough
elevation data could decisively help to stress the difference of the
physical thickness of the atmosphere and consequently help to adjust the
optical thickness components t r t p and t w
for each pixel as well as to monitor the changes of the scaleheights of
E g E d and L p with the elevation of each
pixel. A course topographic model as we have used would help to modify and
improve the enhanced reflectance images to 3-4 counts. The
coarseness of spatial and quantization resolution of the DTM data may not
help to raise the correction accuracy for rugged mountain area, since the
slope the slope-aspect geometry is not a Gaussian distribution (Teillet
1986). The digital elevation data used in this experiment were created by
digitizing contour lines of the UTM map sheet at 1:50 000 scale and
linearly interpolated between contour lines. The terrain slope s and
aspect a can be derived with reference to the neibouring pixels. The solar
incidence angle to the surface normal is expressed by: cosi
=cos qo coss +sin qosincos( fo-a) s= terrain slope , a = terrain
aspect (azimuth) There are three optional applications for the
elevation data in the algorithms:
- In absence of elevation data the average elevation of the subscene
as well the elevation of the reference water bodies are used.
- when a coarse elevation model is available and the topography is
rather complicated used for the adjustment of the optical thickness and
illumination conditions for each pixel.
- when accurate elevation data could be obtained or the areas of
internet are not so complicated as to demand an accurate topographic
model it is worth to transfer the data in to a slope aspect format and
both the optical thickness and illumination geometry expressed by cosi
and g could be considered in our study after such correction the mean
square of spectral features of the some targets were reduced by about
30%.
Result and discussionThe aerosol content, its
thickness and distribution atmosphere are the main problem atmospheric
correction .The visibility codes 1,2,4 indicates the stability of
atmosphere at the time of the observation and the tp and Lp values hence
obtained were quite reliable but the adjustment tp are over estimated the
zero reflectance pixels were not exactly found because of negligence of
wind speed and diffuse irradiance on the water interpreted due to partial
shading of the pixels date 3 had pixel values approached and the
interpreted visibility is only 7.5 Km the adjustment of dark pixel values
approached the real value and improved the result for a clear stable
atmosphere the visual range codes seemed to be more reliable but if the
recorded visual ranges changed abruptly the dark pixel helped to approach
the real value than interpolated value.
Table 2. The extroatmospheric solar irradiance
Eo are sin earth distance adjusted. The global spectral
irradiance Eg diffuse spectral irradiance Ed and spectral
path radiance Lp* are the values at sea level the
scale heights of Eg* Ed Lp are also
justed with the pixel respectively
Parameter |
TM1 |
TM2 |
TM3 |
TM4 |
TM5 |
TM7 |
date 1 (4/27) |
Eo(mWcm-2um-1) |
193.21 |
180.57 |
153.72 |
103.36 |
21.65 |
7.35 |
Eg(mWcm-2um-1) |
106.03 |
102.49 |
91.11 |
62.61 |
12.81 |
4.45 |
Ed(mWcm-2um-1) |
27.03 |
21.49 |
16.22 |
9.24 |
1.30 |
0.38 |
Lp*(**um-1sr-1) |
1.1814 |
0.4247 |
0.1811 |
0.1213 |
0.0099 |
0.0019 |
Lp*(**um-1sr-1) |
1.9415 |
0.7823 |
0.3619 |
0.2623 |
0.0261 |
0.0052 |
Egscale(m) |
-38569 |
-50997 |
-65349 |
-89163 |
-101761 |
-127130 |
Edscale(m) |
1754 |
1542 |
1439 |
1366 |
1283 |
1267 |
Lp Scale(m) |
1482 |
1384 |
1341 |
1395 |
1287 |
1265 |
date 2 (5/13) |
Eo(mWcm-2um-1) |
191.67 |
179.14 |
152.49 |
102.54 |
21.47 |
7.49 |
Eg (mWcm-2um-1) |
115.77 |
111.43 |
98.80 |
67.38 |
13.61 |
4.76 |
Ed (mWcm-2um-1) |
31.55 |
24.93 |
18.68 |
10.53 |
1.46 |
0.43 |
Lp(**um-1sr-1) |
1.7235 |
0.6813 |
0.3016 |
0.2514 |
0.0208 |
0.0039 |
Lp*(**um-1sr-1) |
2.1155 |
0.8612 |
0.3887 |
0.3241 |
0.0277 |
0.0053 |
Egs scale (m) |
-40923 |
-53979 |
-68640 |
-92234 |
-91231 |
-117572 |
Edscale (m) |
1806 |
1576 |
1461 |
1381 |
1289 |
1271 |
Lp Scale(m) |
1459 |
1372 |
1406 |
1406 |
1294 |
1270 |
date 3 (7/9) |
Eo(mWcm-2um-1) |
189.23 |
176.86 |
150.55 |
101.24 |
21.20 |
7.20 |
EgmWcm-2um-1) |
117.20 |
112.71 |
99.85 |
65.76 |
12.37 |
4.50 |
EdmWcm-2um-1) |
39.74 |
31.85 |
23.89 |
13.36 |
1.72 |
0.53 |
Lp(**um-1sr-1) |
5.4500 |
2.1598 |
0.8805 |
0.9670 |
0.0480 |
0.0071 |
Lp*(**um-1sr-1) |
2.6805 |
1.0984 |
0.4522 |
0.5544 |
0.0269 |
0.0039 |
Egscale(m) |
-36276 |
-46297 |
-56874 |
-69934 |
-49391 |
-66263 |
Edscale(m) |
1837 |
1609 |
1492 |
1424 |
1328 |
13.01 |
Lp Scale(m) |
1302 |
1267 |
1228 |
1424 |
1319 |
1278 |
date 4 (9/2) |
Eo (mWcm-2um-1) |
192.31 |
179.73 |
153.00 |
102.89 |
21.55 |
7.32 |
Eg (mWcm-2um-1) |
91.18 |
88.86 |
79.27 |
52.92 |
10.20 |
3.67 |
Ed (mWcm-2um-1 |
17.01 |
13.43 |
10.12 |
5.81 |
0.74 |
0.22 |
Lp (**um-1sr-1 |
1.1681 |
0.4255 |
0.1659 |
0.1785 |
0.0077 |
0.0011 |
Lp* (**um-1sr-1) |
1.4018 |
0.5345 |
0.2173 |
0.2373 |
0.0110 |
0.0015 |
Eg scale(m) |
-39656 |
-54371 |
-70899 |
-83554 |
-63013 |
-86801 |
Ed scale(m) |
1661 |
1465 |
1375 |
1348 |
1272 |
1255 |
Lp scale(m) |
1670 |
1509 |
1392 |
1457 |
1286 |
1254 | Table 2 listed the sea
level values of E d and E g and L p and
their scale heights diffuse spectral irradiance E d and spectral
path radiance L p will decrease with elevation while the global
spectral irradiance E g increases with elevation. The
introduction of scale height for these three parameters simplified the
computation of their modification due to elevation variation it has been
examined that error committed by using scale height method is only one per
thousand compared with applying more complicated algorithms. Clear
lakes of relative stable reflectance were selected for comparison of
correction result the obvious atmospheric between original counts were
greatly compressed(Table 3).
Table 3. Comparison of original values and corrected
reflectance for relative stable object (clear lakes)
|
TM1 |
TM2 |
TM3 |
TM4 |
TM5 |
TM7 |
average original counts |
date 1 |
53.8 |
16.6 |
11.5 |
9.2 |
4.7 |
3.6 |
date 2 |
57.7 |
18.2 |
13.7 |
10.6 |
6.1 |
3.8 |
date3 |
63.5 |
19.7 |
15.9 |
11.4 |
7.2 |
3.9 |
date 4 |
41.1 |
13.5 |
9.4 |
6.3 |
3 |
3.0 |
Corrected reflectance |
date 1 |
0.0539 |
0.425 |
0.0266 |
0.0000 |
0.0001 |
0.0000 |
date 2 |
0.533 |
0.414 |
0.0266 |
0.0000 |
0. 0000 |
0.0000 |
date 3 |
0.549 |
0.0403 |
0.0259 |
0.0000 |
0.0000 |
0.0000 |
date 4 |
0.0556 |
0.0401 |
0.273 |
0.0000 |
0.0000 |
0.0000 | The following conclusion
can be derived from this study:
- The comprehensive correction to remotely sensed data for atmospheric
and georadiometric distortion is feasible the converted reflectance
stable reflectance objects showed an excellent conformity how ever the
degree of correction accuracy on the precision of the input data if a
even radioactive transfer model and a precise correction equation are
used.
- The meteorological record could be used to estimate the components
of optical thickness and to make clear distribution of both direct solar
and diffuse irradiance the path radiance Lp should be estimated by using
multiple methods for comparison since the visibility observation in
comparison among transfer models is also beneficial.
- A georadiometric correction may be an option if a reliable digital
terrain model is not available such a model could be used for both
adjusting the topography dependent atmospheric coefficients and for
correcting the surface illumination conditions.
- For the enhancements of reflectance images the forest reflectance
limits fora biophysical areas need to be recertified from sufficient TM
scenes and added to the procedure the correct decision of the
reflectance limits would guarantee color balance color products.
- Only for a solar zenith angle of less than 33 degree or so the
topographic effect can be removed by including a slope model relative
standardization of reflectance images can be expected at present due to
the estimation and approximation nature of the parameters and due to the
gap between the prerequisites for an accurate and the data
available.
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